Claim FPRD-D16

Exact statement

A capacity-witnessed fixed-envelope recoding consists of a nonempty finite output alphabet Sigma, a positive block width m, a base j at least two, a finite matched source-bracket alphabet with at most j to the m pair types, one m-letter output block for each source bracket, and one distinct m-digit code for each matched pair; its envelope alphabet has symbols (polarity, current output, mate output, digit), matches by reversing polarity and the two output fields, reads the current output field, and replaces each source bracket by one length-m envelope block.

Statusdefinition

External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

This row is imported exactly from the governed FPRD claims ledger. The matrix assignment records normalized inventory coverage; it is not a new proof or a promotion of the ledger status.

Proof or evidence

The ledger points to docs/specs/m19-fixed-envelope-recoding.md. The matrix has not yet rewritten that source into a self-contained public proof summary.

docs/specs/m19-fixed-envelope-recoding.md →

Verification notes

Reviewed on 2026-08-25 for identifier, status, provenance, evidence-link presence, and dependency import only. Mathematical proof audit remains the next action unless separately documented.

Limitations

The witness makes the source paper's decisive positional-coding seam executable without folding the preceding arbitrary-CFG normalization or its hidden asymptotic constants into M19.

Open work

Add a self-contained definition page with examples, nonexamples, and dependency boundaries.

Notes

The witness makes the source paper's decisive positional-coding seam executable without folding the preceding arbitrary-CFG normalization or its hidden asymptotic constants into M19.